Question

laplace transform of sin2t cost
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Answer 1

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Answer 2

Given:

Consider the given function is sin 2t. cost

Find:

Laplace tranfrom of the fucntion

Solution:

Sin2t = 2 sint cost

Therefore

sin 2t. cost = 2 sint cos t. cost

sin 2t. cost = 2sint (cos^2t)

sin 2t. cost = 2sint (1-sin^2t)

sin 2t. cost = 2sint -2sin^3t

applying laplace on both sides we get

$L^{-1}(sin2tcost)=L^{-1}(2sint-2sin^3t)$

$L^{-1}(sin2tcost)=2L^{-1}(sint)+2L^{-1}(sin^3t)$

$L^{-1}(sin2tcost)=-\frac{3}{2(s^2+9)}+\frac{7}{2(s^2+1)}$